{"total":102,"rows":[{"id":"2210.15651","title":"Learning Single-Index Models with Shallow Neural Networks","created":"2022-10-27","cited_by_count":92,"area":null},{"id":"2208.12591","title":"On the Implicit Bias in Deep-Learning Algorithms","created":"2022-08-26","cited_by_count":86,"area":null},{"id":"2206.00939","title":"Gradient flow dynamics of shallow ReLU networks for square loss and orthogonal inputs","created":"2022-06-02","cited_by_count":76,"area":null},{"id":"2105.03361","title":"What Kinds of Functions do Deep Neural Networks Learn? Insights from Variational Spline Theory","created":"2021-05-07","cited_by_count":60,"area":null},{"id":"2201.12760","title":"Implicit Regularization Towards Rank Minimization in ReLU Networks","created":"2022-01-30","cited_by_count":53,"area":null},{"id":"2109.09710","title":"Understanding neural networks with reproducing kernel Banach spaces","created":"2021-09-20","cited_by_count":50,"area":null},{"id":"2106.15002","title":"Characterization of the Variation Spaces Corresponding to Shallow Neural Networks","created":"2021-06-28","cited_by_count":48,"area":null},{"id":"2109.08844","title":"Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks","created":"2021-09-18","cited_by_count":41,"area":null},{"id":"2209.15055","title":"Implicit Bias of Large Depth Networks: a Notion of Rank for Nonlinear Functions","created":"2022-09-29","cited_by_count":38,"area":null},{"id":"2205.08078","title":"Unraveling Attention via Convex Duality: Analysis and Interpretations of Vision Transformers","created":"2022-05-17","cited_by_count":30,"area":null},{"id":"2109.03810","title":"Scaled ReLU Matters for Training Vision Transformers","created":"2021-09-08","cited_by_count":29,"area":null},{"id":"2203.03756","title":"Flat minima generalize for low-rank matrix recovery","created":"2022-03-07","cited_by_count":28,"area":null},{"id":"2110.05518","title":"Global Optimality Beyond Two Layers: Training Deep ReLU Networks via Convex Programs","created":"2021-10-11","cited_by_count":25,"area":null},{"id":"2306.08321","title":"Nonparametric regression using over-parameterized shallow ReLU neural networks","created":"2023-06-14","cited_by_count":24,"area":null},{"id":"2103.01499","title":"Demystifying Batch Normalization in ReLU Networks: Equivalent Convex Optimization Models and Implicit Regularization","created":"2021-03-02","cited_by_count":21,"area":null},{"id":"2205.09072","title":"On the Effective Number of Linear Regions in Shallow Univariate ReLU Networks: Convergence Guarantees and Implicit Bias","created":"2022-05-18","cited_by_count":21,"area":null},{"id":"2301.09554","title":"Deep Learning Meets Sparse Regularization: A Signal Processing Perspective","created":"2023-01-23","cited_by_count":21,"area":null},{"id":"2405.16391","title":"When does compositional structure yield compositional generalization? A kernel theory","created":"2024-05-26","cited_by_count":20,"area":null},{"id":"2303.01353","title":"Penalising the biases in norm regularisation enforces sparsity","created":"2023-03-02","cited_by_count":19,"area":null},{"id":"2102.12238","title":"Inductive Bias of Multi-Channel Linear Convolutional Networks with Bounded Weight Norm","created":"2021-02-24","cited_by_count":18,"area":null},{"id":"2305.16534","title":"Variation Spaces for Multi-Output Neural Networks: Insights on Multi-Task Learning and Network Compression","created":"2023-05-25","cited_by_count":18,"area":null},{"id":"2205.11787","title":"Quadratic models for understanding catapult dynamics of neural networks","created":"2022-05-24","cited_by_count":17,"area":null},{"id":"2205.15809","title":"Feature Learning in $L_{2}$-regularized DNNs: Attraction/Repulsion and Sparsity","created":"2022-05-31","cited_by_count":17,"area":null},{"id":"2202.00856","title":"The Role of Linear Layers in Nonlinear Interpolating Networks","created":"2022-02-02","cited_by_count":16,"area":null},{"id":"2305.15141","title":"From Tempered to Benign Overfitting in ReLU Neural Networks","created":"2023-05-24","cited_by_count":16,"area":null},{"id":"2306.06479","title":"Learning a Neuron by a Shallow ReLU Network: Dynamics and Implicit Bias for Correlated Inputs","created":"2023-06-10","cited_by_count":16,"area":null},{"id":"2304.01561","title":"Optimal rates of approximation by shallow ReLU$^k$ neural networks and applications to nonparametric regression","created":"2023-04-04","cited_by_count":15,"area":null},{"id":"2203.01631","title":"Fully-Connected Network on Noncompact Symmetric Space and Ridgelet Transform based on Helgason-Fourier Analysis","created":"2022-03-03","cited_by_count":14,"area":null},{"id":"2111.02278","title":"Mean-field Analysis of Piecewise Linear Solutions for Wide ReLU Networks","created":"2021-11-03","cited_by_count":13,"area":null},{"id":"2505.20172","title":"A Theoretical Framework for Grokking: Interpolation followed by Riemannian Norm Minimisation","created":"2025-05-26","cited_by_count":13,"area":null},{"id":"2211.11052","title":"Convexifying Transformers: Improving optimization and understanding of transformer networks","created":"2022-11-20","cited_by_count":12,"area":null},{"id":"2406.06838","title":"Stable Minima Cannot Overfit in Univariate ReLU Networks: Generalization by Large Step Sizes","created":"2024-06-10","cited_by_count":12,"area":null},{"id":"2205.14819","title":"Universality of Group Convolutional Neural Networks Based on Ridgelet Analysis on Groups","created":"2022-05-30","cited_by_count":11,"area":null},{"id":"2307.15396","title":"Noisy Interpolation Learning with Shallow Univariate ReLU Networks","created":"2023-07-28","cited_by_count":11,"area":null},{"id":"2101.09849","title":"Deep Learning Generalization and the Convex Hull of Training Sets","created":"2021-01-25","cited_by_count":10,"area":null},{"id":"2204.09664","title":"Deep Learning meets Nonparametric Regression: Are Weight-Decayed DNNs Locally Adaptive?","created":"2022-04-20","cited_by_count":10,"area":null},{"id":"2109.12960","title":"Ridgeless Interpolation with Shallow ReLU Networks in $1D$ is Nearest Neighbor Curvature Extrapolation and Provably Generalizes on Lipschitz Functions","created":"2021-09-27","cited_by_count":9,"area":null},{"id":"2310.02396","title":"Inductive biases of multi-task learning and finetuning: multiple regimes of feature reuse","created":"2023-10-03","cited_by_count":9,"area":null},{"id":"2311.06748","title":"How do Minimum-Norm Shallow Denoisers Look in Function Space?","created":"2023-11-12","cited_by_count":9,"area":null},{"id":"2412.18283","title":"On the Local Complexity of Linear Regions in Deep ReLU Networks","created":"2024-12-24","cited_by_count":9,"area":null},{"id":"2104.07531","title":"On Energy-Based Models with Overparametrized Shallow Neural Networks","created":"2021-04-15","cited_by_count":8,"area":null},{"id":"2305.15598","title":"ReLU Neural Networks with Linear Layers are Biased Towards Single- and Multi-Index Models","created":"2023-05-24","cited_by_count":8,"area":null},{"id":"2403.08750","title":"Neural reproducing kernel Banach spaces and representer theorems for deep networks","created":"2024-03-13","cited_by_count":8,"area":null},{"id":"2404.18769","title":"Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks","created":"2024-04-29","cited_by_count":8,"area":null},{"id":"2106.04770","title":"Ghosts in Neural Networks: Existence, Structure and Role of Infinite-Dimensional Null Space","created":"2021-06-09","cited_by_count":7,"area":null},{"id":"2312.12657","title":"The Convex Landscape of Neural Networks: Characterizing Global Optima and Stationary Points via Lasso Models","created":"2023-12-19","cited_by_count":7,"area":null},{"id":"2507.07207","title":"Scaling can lead to compositional generalization","created":"2025-07-09","cited_by_count":7,"area":null},{"id":"2307.13147","title":"Extending Path-Dependent NJ-ODEs to Noisy Observations and a Dependent Observation Framework","created":"2023-07-24","cited_by_count":6,"area":null},{"id":"2201.01873","title":"NeuralMLS: Geometry-Aware Control Point Deformation","created":"2022-01-05","cited_by_count":5,"area":null},{"id":"2202.00790","title":"On Regularizing Coordinate-MLPs","created":"2022-02-01","cited_by_count":5,"area":null},{"id":"2206.05317","title":"Intrinsic dimensionality and generalization properties of the $\\mathcal{R}$-norm inductive bias","created":"2022-06-10","cited_by_count":5,"area":null},{"id":"2209.09658","title":"Lazy vs hasty: linearization in deep networks impacts learning schedule based on example difficulty","created":"2022-09-19","cited_by_count":5,"area":null},{"id":"2307.01177","title":"Neural Hilbert Ladders: Multi-Layer Neural Networks in Function Space","created":"2023-07-03","cited_by_count":5,"area":null},{"id":"2310.03696","title":"Function-Space Optimality of Neural Architectures with Multivariate Nonlinearities","created":"2023-10-05","cited_by_count":5,"area":null},{"id":"2312.08461","title":"Space-Time Approximation with Shallow Neural Networks in Fourier Lebesgue spaces","created":"2023-12-13","cited_by_count":5,"area":null},{"id":"2406.02529","title":"ReLUs Are Sufficient for Learning Implicit Neural Representations","created":"2024-06-04","cited_by_count":5,"area":null},{"id":"2511.20888","title":"Deep Learning as a Convex Paradigm of Computation: Minimizing Circuit Size with ResNets","created":"2025-11-25","cited_by_count":5,"area":null},{"id":"2602.20062","title":"A Theory of How Pretraining Shapes Inductive Bias in Fine-Tuning","created":"2026-02-23","cited_by_count":5,"area":null},{"id":"2112.06209","title":"Measuring Complexity of Learning Schemes Using Hessian-Schatten Total Variation","created":"2021-12-12","cited_by_count":4,"area":null},{"id":"2112.15577","title":"How Infinitely Wide Neural Networks Can Benefit from Multi-task Learning -- an Exact Macroscopic Characterization","created":"2021-12-31","cited_by_count":4,"area":null},{"id":"2206.14625","title":"From Kernel Methods to Neural Networks: A Unifying Variational Formulation","created":"2022-06-29","cited_by_count":4,"area":null},{"id":"2110.03673","title":"Tighter Sparse Approximation Bounds for ReLU Neural Networks","created":"2021-10-07","cited_by_count":3,"area":null},{"id":"2311.06138","title":"Minimum norm interpolation by perceptra: Explicit regularization and implicit bias","created":"2023-11-10","cited_by_count":3,"area":null},{"id":"2402.08808","title":"Depth Separation in Norm-Bounded Infinite-Width Neural Networks","created":"2024-02-13","cited_by_count":3,"area":null},{"id":"2605.19458","title":"Implicit Bias of Mirror Flow in Homogeneous Neural Networks: Sparse and Dense Feature Learning","created":"2026-05-19","cited_by_count":3,"area":null},{"id":"2102.13522","title":"Experiments with Rich Regime Training for Deep Learning","created":"2021-02-26","cited_by_count":2,"area":null},{"id":"2112.11157","title":"Integral representations of shallow neural network with Rectified Power Unit activation function","created":"2021-12-20","cited_by_count":2,"area":null},{"id":"2112.13542","title":"Sparsest Univariate Learning Models Under Lipschitz Constraint","created":"2021-12-27","cited_by_count":2,"area":null},{"id":"2210.03069","title":"PathProx: A Proximal Gradient Algorithm for Weight Decay Regularized Deep Neural Networks","created":"2022-10-06","cited_by_count":2,"area":null},{"id":"2309.02422","title":"Integral Probability Metrics Meet Neural Networks: The Radon-Kolmogorov-Smirnov Test","created":"2023-09-05","cited_by_count":2,"area":null},{"id":"2402.15984","title":"A unified Fourier slice method to derive ridgelet transform for a variety of depth-2 neural networks","created":"2024-02-25","cited_by_count":2,"area":null},{"id":"2410.02132","title":"Nonuniform random feature models using derivative information","created":"2024-10-03","cited_by_count":2,"area":null},{"id":"2410.14591","title":"A Lipschitz spaces view of infinitely wide shallow neural networks","created":"2024-10-18","cited_by_count":2,"area":null},{"id":"2411.09355","title":"Prices, Bids, Values: One ML-Powered Combinatorial Auction to Rule Them All","created":"2024-11-14","cited_by_count":2,"area":null},{"id":"2411.11242","title":"Mirror Descent on Reproducing Kernel Banach Spaces","created":"2024-11-18","cited_by_count":2,"area":null},{"id":"2106.05739","title":"Separation Results between Fixed-Kernel and Feature-Learning Probability Metrics","created":"2021-06-10","cited_by_count":1,"area":null},{"id":"2203.10366","title":"Deep Learning Generalization, Extrapolation, and Over-parameterization","created":"2022-03-19","cited_by_count":1,"area":null},{"id":"2303.07874","title":"Bayes Complexity of Learners vs Overfitting","created":"2023-03-13","cited_by_count":1,"area":null},{"id":"2307.14373","title":"Piecewise Linear Functions Representable with Infinite Width Shallow ReLU Neural Networks","created":"2023-07-25","cited_by_count":1,"area":null},{"id":"2311.15404","title":"Applying statistical learning theory to deep learning","created":"2023-11-26","cited_by_count":1,"area":null},{"id":"2403.01046","title":"A Library of Mirrors: Deep Neural Nets in Low Dimensions are Convex Lasso Models with Reflection Features","created":"2024-03-02","cited_by_count":1,"area":null},{"id":"2405.18410","title":"Towards a Sampling Theory for Implicit Neural Representations","created":"2024-05-28","cited_by_count":1,"area":null},{"id":"2505.22578","title":"Favorability of Loss Landscape with Weight Decay Requires Both Large Overparametrization and Initialization","created":"2025-05-28","cited_by_count":1,"area":null},{"id":"2601.16070","title":"On damage of interpolation to adversarial robustness in regression","created":"2026-01-22","cited_by_count":1,"area":null},{"id":"2603.10079","title":"Large Spikes in Stochastic Gradient Descent: A Large-Deviations View","created":"2026-03-10","cited_by_count":1,"area":null},{"id":"2603.17785","title":"A Dual Certificate Approach to Sparsity in Infinite-Width Shallow Neural Networks","created":"2026-03-18","cited_by_count":1,"area":null},{"id":"2607.06382","title":"A Function-Space Dichotomy for Compositional Learning: Exponential Sub-Optimality of the Neural Tangent Kernel","created":"2026-07-07","cited_by_count":1,"area":null},{"id":"2304.06959","title":"Convex Dual Theory Analysis of Two-Layer Convolutional Neural Networks with Soft-Thresholding","created":"2023-04-14","cited_by_count":0,"area":null},{"id":"2410.21696","title":"The Effects of Multi-Task Learning on ReLU Neural Network Functions","created":"2024-10-29","cited_by_count":0,"area":null},{"id":"2503.10587","title":"The Spectral Bias of Shallow Neural Network Learning is Shaped by the Choice of Non-linearity","created":"2025-03-13","cited_by_count":0,"area":null},{"id":"2505.21791","title":"Global Minimizers of $\\ell^p$-Regularized Objectives Yield the Sparsest ReLU Neural Networks","created":"2025-05-27","cited_by_count":0,"area":null},{"id":"2506.07884","title":"Schauder Bases for $C[0, 1]$ Using ReLU, Softplus and Two Sigmoidal Functions","created":"2025-06-09","cited_by_count":0,"area":null},{"id":"2506.11357","title":"Generalization Bound of Gradient Flow through Training Trajectory and Data-dependent Kernel","created":"2025-06-12","cited_by_count":0,"area":null},{"id":"2601.03919","title":"A Gap Between Decision Trees and Neural Networks","created":"2026-01-07","cited_by_count":0,"area":null},{"id":"2604.23260","title":"Explicit integral representations and quantitative bounds for two-layer ReLU networks","created":"2026-04-25","cited_by_count":0,"area":null},{"id":"2605.25134","title":"Theoretical Analysis of Sparse Optimization with Reparameterization, Weight Decay, and Adaptive Learning Rate","created":"2026-05-24","cited_by_count":0,"area":null},{"id":"2606.04754","title":"Beyond Structural Symmetries: Linear Mode Connectivity via Neuron Identifiability","created":"2026-06-03","cited_by_count":0,"area":null},{"id":"2608.04382","title":"Non-asymptotic implicit bias of logistic regression at early-stage gradient descent dynamics","created":"2026-08-05","cited_by_count":0,"area":null},{"id":"2608.17434","title":"Depth Enables Local Entropy: Quadratic Depth Dependence in Deep Variation-Norm ReLU Regression","created":"2026-08-18","cited_by_count":0,"area":null},{"id":"2609.05263","title":"Shallow neural network approximation in mixed Sobolev spaces","created":"2026-09-04","cited_by_count":0,"area":null}],"next_cursor":"100"}